The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-Neumann map) of the measured data of some physical quantity on the boundary of the medium. It is based on the sequence of special solutions of the governing equation for the background medium related to a singular solution of the equation. In this paper the blowup property of the sequence is clarified. Moreover a new formulation of the probe method based on the property is given in some typical inverse boundary value problems.

We investigated the relationship among the number of flash annealing times to obtain Si clean surface and the change of arsenic dopant concentration and subband levels using secondary ion mass spectroscopy (SIMS) and angle-resolved photoelectron spectroscopy(ARPES). The SIMS result shows that the first five times of the flash annealing already induces significant reduction of the dopant concentration in agreement with the recent work [Pitter et al., J. Vac. Sci. Technol. B 30, 021806 (2012)]. We found the energies of hole subband levels rapidly decrease as the number of the flash annealing times increases. We calculated the subband levels in a broadened confinement potential taking the dopant reduction determined by SIMS into account. The energy separations of the calculated subband levels were in good agreement with the ARPES results.

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